UNLIKELY INTERSECTIONS IN FINITE CHARACTERISTIC

UNLIKELY INTERSECTIONS IN FINITE CHARACTERISTIC

We present a heuristic argument based on Honda-Tate theory against many conjectures in 'unlikely intersections' over the algebraic closure of a finite field; notably, we conjecture that every abelian variety of dimension 4 is isogenous to a Jacobian. Using methods of additive combinatorics...

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Bibliographic Details
Main Authors: Shankar, Ananth (Author), Tsimerman, Jacob (Author)
Other Authors: Massachusetts Institute of Technology. Department of Mathematics (Contributor)
Format: Article
Language:English
Published: Cambridge University Press (CUP), 2019-11-07T18:06:42Z.
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Online Access:Get fulltext
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100 1 0 |a Shankar, Ananth  |e author 
100 1 0 |a Massachusetts Institute of Technology. Department of Mathematics  |e contributor 
700 1 0 |a Tsimerman, Jacob  |e author 
245 0 0 |a UNLIKELY INTERSECTIONS IN FINITE CHARACTERISTIC 
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856 |z Get fulltext  |u https://hdl.handle.net/1721.1/122793 
520 |a We present a heuristic argument based on Honda-Tate theory against many conjectures in 'unlikely intersections' over the algebraic closure of a finite field; notably, we conjecture that every abelian variety of dimension 4 is isogenous to a Jacobian. Using methods of additive combinatorics, we answer a related question of Chai and Oort where the ambient Shimura variety is a power of the modular curve. 
655 7 |a Article 
773 |t Forum of Mathematics, Sigma 

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